The Pantheon we see today, with its grandiose dome and marbles, was built by the emperor Trajan, as shown by the brick stamps of 113-114 AD found in the outer walls during the most recent restorations.
The building was completed by Hadrian, who kept the ancient dedicatory inscription of Marcus Agrippa on the façade, as we know from the Historia Augusta (S.H.A., XIX,9)
M(arcus) AGRIPPA L(uci) F(ilius) CO(n)S(ul) TERTIVM FECIT.
So before the current Pantheon there was an older one, built at the end of the 1st century BC by the consul Marcus Vipsanius Agrippa, son-in-law of Augustus (he had married his only daughter Julia).
Agrippa was the best general and main ally of Augustus: he was the leader of the historic victory of Actium over Mark Antony and Cleopatra, which gave start to the principality of Augustus and laid the foundations of the empire.
The inscription kept by Hadrian (Marcus Agrippa, son of Lucius, consul for the third time, made), tells us that the first Pantheon was dedicated by Agrippa between 27 and 25 BC.
For years it was thought that the entrance of Agrippa's Pantheon was oriented towards the south instead of the north, and that it had a large dome similar to the current one.
Recent excavations have disproved those theories, because under the current pronaos the pronaos of Agrippa's Pantheon was found: it had ten columns instead of the eight ones we see today, and the entrance was on the same side, to the north, as it is now.
Further explorations have found traces of the foundations of the original circular perimeter wall, which had more or less the same diameter; but the thickness of the walls could not to support the weight of a masonry dome of that size.
It should also be noted that the first domes made with concrete were built at the end of the 1st century BC, and their size was much smaller.
Therefore, there was no practical experience nor the technical skills necessary to build a masonry dome of that size already at the time of Agrippa.
You can discover these and other secrets about the building techniques of Agrippa's Pantheon and that of Trajan and Hadrian in Marina De Franceschini's book «Pantheon. Architecture and Light», also in English edition.